Sainsbury's has had an undisclosed approach for the £1 billion-valued group that owns Argos and DIY chain Homebase rejected.
The supermarket said it made an initial approach for Home Retail Group in November and is still deciding whether to table a former offer.
The supermarket, which made the approach amid an industry price war, said a combination of the two stores would create a strong food and non-food retailer with strong heritages.
Shares in Home Retail jumped 34% after details of the November approach emerged, while Sainsbury's stock slipped more than 3%.
Sainsbury's underlying pre-tax profit was down 17.9% to £308 million, results from the supermarket revealed on Wednesday.
Like-for-like sales were down 1.6% in the 28 weeks to September 26, while underlying group sales were down 2% to £13.6 million, compared to £13.9m in the same period last year.
Sainsbury's chief executive Mike Coupe said: “The grocery retail marketplace remains challenging but Sainsbury’s is a great business, run by an experienced management team, supported by talented colleagues and strong values.
"I am confident we are making progress and we are looking forward to a successful Christmas, offering our customers fantastic products and great value."
Sainsbury's has announced its first drop in profits in a decade as it counts the cost of "unprecedented" change in the supermarket industry.
The UK's third biggest grocer racked up a profit of #681 million for the year to March 14 - a 14.7% decline on a year earlier after a period in which like-for-like sales dropped 1.9%.
Chief executive Mike Coupe said: "The UK marketplace is changing faster than at any time in the past 30 years which has impacted our profits, like-for-like sales and market share."
The company also cut its full-year dividend for shareholders by 23.7%.
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Supermarket chain Sainsbury's has reported a fifth successive quarter of falling sales and said it expects conditions to remain challenging for the "foreseeable future".
Sainsbury's, which has 597 supermarkets and 707 convenience stores in the UK, posted a 1.9% decline in like-for-like sales for the 10 weeks to March 14th, compared with a fall of 1.7% in the previous quarter.
The company is about to report the first drop in annual profits in a decade and chief executive Mike Coupe warned today there were no immediate signs of a let-up in the price squeeze facing the sector.
He said: "Food deflation is likely to persist for the rest of this calendar year, and competitive pressures on price will continue."
Sainsbury's will report full-year profits in May and they are expected to show their first fall after nine years of growth under former head Justin King, with City analysts expecting a 17% decline to £659 million.
Sainsbury's said like-for-like sales fell 1.7% in the 14 weeks to January 3 and boss Mike Coupe said the outlook remained "challenging".
He said a fall in food prices was likely to continue, but said the performance in the third quarter showed an "improving trend".
Sales had dipped 2.8% in the second quarter.
Sainsbury's said it enjoyed a record-breaking week before Christmas with 29.5 million customer transactions.
Sainsbury's has provided a great Christmas for our customers. Food price deflation and falling fuel prices have enabled our customers to treat themselves over the festive period.
The outlook for the remainder of the financial year is set to remain challenging, with food price deflation likely to continue.
Sainsbury's has said it will reduce spending on new stores and look into more cost-saving methods to help finance price cuts in an effort to cope with the toughest market conditions for decades.
Sainsbury's posted a profit before tax and one off items of £375 million for the six months to 27th Sept. This figure is ahead of analysts' expectations of about £350 million, but down from £400 million in the same period last year.
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